1 {-# OPTIONS_GHC -XNoImplicitPrelude #-}
2 -----------------------------------------------------------------------------
5 -- Copyright : (c) The University of Glasgow 2001
6 -- License : BSD-style (see the file libraries/base/LICENSE)
8 -- Maintainer : libraries@haskell.org
9 -- Stability : experimental
10 -- Portability : portable
12 -- This module defines bitwise operations for signed and unsigned
13 -- integers. Instances of the class 'Bits' for the 'Int' and
14 -- 'Integer' types are available from this module, and instances for
15 -- explicitly sized integral types are available from the
16 -- "Data.Int" and "Data.Word" modules.
18 -----------------------------------------------------------------------------
22 (.&.), (.|.), xor, -- :: a -> a -> a
23 complement, -- :: a -> a
24 shift, -- :: a -> Int -> a
25 rotate, -- :: a -> Int -> a
27 setBit, -- :: a -> Int -> a
28 clearBit, -- :: a -> Int -> a
29 complementBit, -- :: a -> Int -> a
30 testBit, -- :: a -> Int -> Bool
31 bitSize, -- :: a -> Int
32 isSigned, -- :: a -> Bool
33 shiftL, shiftR, -- :: a -> Int -> a
34 rotateL, rotateR -- :: a -> Int -> a
38 -- instance Bits Integer
41 -- Defines the @Bits@ class containing bit-based operations.
42 -- See library document for details on the semantics of the
43 -- individual operations.
45 #if defined(__GLASGOW_HASKELL__) || defined(__HUGS__)
49 #ifdef __GLASGOW_HASKELL__
59 infixl 8 `shift`, `rotate`, `shiftL`, `shiftR`, `rotateL`, `rotateR`
65 The 'Bits' class defines bitwise operations over integral types.
67 * Bits are numbered from 0 with bit 0 being the least
70 Minimal complete definition: '.&.', '.|.', 'xor', 'complement',
71 ('shift' or ('shiftL' and 'shiftR')), ('rotate' or ('rotateL' and 'rotateR')),
72 'bitSize' and 'isSigned'.
74 class Num a => Bits a where
84 {-| Reverse all the bits in the argument -}
87 {-| @'shift' x i@ shifts @x@ left by @i@ bits if @i@ is positive,
88 or right by @-i@ bits otherwise.
89 Right shifts perform sign extension on signed number types;
90 i.e. they fill the top bits with 1 if the @x@ is negative
93 An instance can define either this unified 'shift' or 'shiftL' and
94 'shiftR', depending on which is more convenient for the type in
96 shift :: a -> Int -> a
98 x `shift` i | i<0 = x `shiftR` (-i)
102 {-| @'rotate' x i@ rotates @x@ left by @i@ bits if @i@ is positive,
103 or right by @-i@ bits otherwise.
105 For unbounded types like 'Integer', 'rotate' is equivalent to 'shift'.
107 An instance can define either this unified 'rotate' or 'rotateL' and
108 'rotateR', depending on which is more convenient for the type in
110 rotate :: a -> Int -> a
112 x `rotate` i | i<0 = x `rotateR` (-i)
113 | i>0 = x `rotateL` i
117 -- Rotation can be implemented in terms of two shifts, but care is
118 -- needed for negative values. This suggested implementation assumes
119 -- 2's-complement arithmetic. It is commented out because it would
120 -- require an extra context (Ord a) on the signature of 'rotate'.
121 x `rotate` i | i<0 && isSigned x && x<0
122 = let left = i+bitSize x in
123 ((x `shift` i) .&. complement ((-1) `shift` left))
125 | i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
127 | i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
130 -- | @bit i@ is a value with the @i@th bit set
133 -- | @x \`setBit\` i@ is the same as @x .|. bit i@
134 setBit :: a -> Int -> a
136 -- | @x \`clearBit\` i@ is the same as @x .&. complement (bit i)@
137 clearBit :: a -> Int -> a
139 -- | @x \`complementBit\` i@ is the same as @x \`xor\` bit i@
140 complementBit :: a -> Int -> a
142 -- | Return 'True' if the @n@th bit of the argument is 1
143 testBit :: a -> Int -> Bool
145 {-| Return the number of bits in the type of the argument. The actual
146 value of the argument is ignored. The function 'bitSize' is
147 undefined for types that do not have a fixed bitsize, like 'Integer'.
151 {-| Return 'True' if the argument is a signed type. The actual
152 value of the argument is ignored -}
153 isSigned :: a -> Bool
156 x `setBit` i = x .|. bit i
157 x `clearBit` i = x .&. complement (bit i)
158 x `complementBit` i = x `xor` bit i
159 x `testBit` i = (x .&. bit i) /= 0
161 {-| Shift the argument left by the specified number of bits
162 (which must be non-negative).
164 An instance can define either this and 'shiftR' or the unified
165 'shift', depending on which is more convenient for the type in
167 shiftL :: a -> Int -> a
168 x `shiftL` i = x `shift` i
170 {-| Shift the first argument right by the specified number of bits
171 (which must be non-negative).
172 Right shifts perform sign extension on signed number types;
173 i.e. they fill the top bits with 1 if the @x@ is negative
174 and with 0 otherwise.
176 An instance can define either this and 'shiftL' or the unified
177 'shift', depending on which is more convenient for the type in
179 shiftR :: a -> Int -> a
180 x `shiftR` i = x `shift` (-i)
182 {-| Rotate the argument left by the specified number of bits
183 (which must be non-negative).
185 An instance can define either this and 'rotateR' or the unified
186 'rotate', depending on which is more convenient for the type in
188 rotateL :: a -> Int -> a
189 x `rotateL` i = x `rotate` i
191 {-| Rotate the argument right by the specified number of bits
192 (which must be non-negative).
194 An instance can define either this and 'rotateL' or the unified
195 'rotate', depending on which is more convenient for the type in
197 rotateR :: a -> Int -> a
198 x `rotateR` i = x `rotate` (-i)
200 instance Bits Int where
203 #ifdef __GLASGOW_HASKELL__
204 (I# x#) .&. (I# y#) = I# (word2Int# (int2Word# x# `and#` int2Word# y#))
206 (I# x#) .|. (I# y#) = I# (word2Int# (int2Word# x# `or#` int2Word# y#))
208 (I# x#) `xor` (I# y#) = I# (word2Int# (int2Word# x# `xor#` int2Word# y#))
210 complement (I# x#) = I# (word2Int# (int2Word# x# `xor#` int2Word# (-1#)))
212 (I# x#) `shift` (I# i#)
213 | i# >=# 0# = I# (x# `iShiftL#` i#)
214 | otherwise = I# (x# `iShiftRA#` negateInt# i#)
216 {-# INLINE rotate #-} -- See Note [Constant folding for rotate]
217 (I# x#) `rotate` (I# i#) =
218 I# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
219 (x'# `uncheckedShiftRL#` (wsib -# i'#))))
222 i'# = word2Int# (int2Word# i# `and#` int2Word# (wsib -# 1#))
223 wsib = WORD_SIZE_IN_BITS# {- work around preprocessor problem (??) -}
224 bitSize _ = WORD_SIZE_IN_BITS
226 {-# INLINE shiftR #-}
227 -- same as the default definition, but we want it inlined (#2376)
228 x `shiftR` i = x `shift` (-i)
229 #else /* !__GLASGOW_HASKELL__ */
235 complement = primComplementInt
238 testBit = primTestInt
239 bitSize _ = SIZEOF_HSINT*8
240 #elif defined(__NHC__)
241 (.&.) = nhc_primIntAnd
242 (.|.) = nhc_primIntOr
244 complement = nhc_primIntCompl
245 shiftL = nhc_primIntLsh
246 shiftR = nhc_primIntRsh
251 | i<0 && x<0 = let left = i+bitSize x in
252 ((x `shift` i) .&. complement ((-1) `shift` left))
254 | i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
256 | i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
258 #endif /* !__GLASGOW_HASKELL__ */
263 foreign import ccall nhc_primIntAnd :: Int -> Int -> Int
264 foreign import ccall nhc_primIntOr :: Int -> Int -> Int
265 foreign import ccall nhc_primIntXor :: Int -> Int -> Int
266 foreign import ccall nhc_primIntLsh :: Int -> Int -> Int
267 foreign import ccall nhc_primIntRsh :: Int -> Int -> Int
268 foreign import ccall nhc_primIntCompl :: Int -> Int
271 instance Bits Integer where
272 #if defined(__GLASGOW_HASKELL__)
276 complement = complementInteger
278 -- reduce bitwise binary operations to special cases we can handle
280 x .&. y | x<0 && y<0 = complement (complement x `posOr` complement y)
281 | otherwise = x `posAnd` y
283 x .|. y | x<0 || y<0 = complement (complement x `posAnd` complement y)
284 | otherwise = x `posOr` y
286 x `xor` y | x<0 && y<0 = complement x `posXOr` complement y
287 | x<0 = complement (complement x `posXOr` y)
288 | y<0 = complement (x `posXOr` complement y)
289 | otherwise = x `posXOr` y
291 -- assuming infinite 2's-complement arithmetic
292 complement a = -1 - a
295 shift x i | i >= 0 = x * 2^i
296 | otherwise = x `div` 2^(-i)
298 rotate x i = shift x i -- since an Integer never wraps around
300 bitSize _ = error "Data.Bits.bitSize(Integer)"
303 #if !defined(__GLASGOW_HASKELL__)
304 -- Crude implementation of bitwise operations on Integers: convert them
305 -- to finite lists of Ints (least significant first), zip and convert
308 -- posAnd requires at least one argument non-negative
309 -- posOr and posXOr require both arguments non-negative
311 posAnd, posOr, posXOr :: Integer -> Integer -> Integer
312 posAnd x y = fromInts $ zipWith (.&.) (toInts x) (toInts y)
313 posOr x y = fromInts $ longZipWith (.|.) (toInts x) (toInts y)
314 posXOr x y = fromInts $ longZipWith xor (toInts x) (toInts y)
316 longZipWith :: (a -> a -> a) -> [a] -> [a] -> [a]
317 longZipWith f xs [] = xs
318 longZipWith f [] ys = ys
319 longZipWith f (x:xs) (y:ys) = f x y:longZipWith f xs ys
321 toInts :: Integer -> [Int]
324 | otherwise = mkInt (n `mod` numInts):toInts (n `div` numInts)
325 where mkInt n | n > toInteger(maxBound::Int) = fromInteger (n-numInts)
326 | otherwise = fromInteger n
328 fromInts :: [Int] -> Integer
329 fromInts = foldr catInt 0
330 where catInt d n = (if d<0 then n+1 else n)*numInts + toInteger d
332 numInts = toInteger (maxBound::Int) - toInteger (minBound::Int) + 1
333 #endif /* !__GLASGOW_HASKELL__ */
335 {- Note [Constant folding for rotate]
336 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
337 The INLINE on the Int instance of rotate enables it to be constant
339 sumU . mapU (`rotate` 3) . replicateU 10000000 $ (7 :: Int)
342 \ (ww_sO7 :: Int#) (ww1_sOb :: Int#) ->
343 case ww1_sOb of wild_XM {
344 __DEFAULT -> Main.$wfold (+# ww_sO7 56) (+# wild_XM 1);
346 whereas before it was left as a call to $wrotate.
348 All other Bits instances seem to inline well enough on their
349 own to enable constant folding; for example 'shift':
350 sumU . mapU (`shift` 3) . replicateU 10000000 $ (7 :: Int)
353 \ (ww_sOb :: Int#) (ww1_sOf :: Int#) ->
354 case ww1_sOf of wild_XM {
355 __DEFAULT -> Main.$wfold (+# ww_sOb 56) (+# wild_XM 1);